Computing continuous-time growth models with boundary conditions via wavelets

This paper presents an algorithm for approximating the solution of deterministic/stochastic continuous-time growth models based on the Euler's equation and the transversality conditions. The main issue for computing these models is to deal efficiently with the boundary conditions associated. This approach is a wavelets-collocation method derived from the finite-iterative trapezoidal approach. Illustrative examples are give

Valuation of boundary-linked assets

This article studies the valuation of boundary-linked assets and their derivatives in continuous-time markets. Valuing boundary-linked assets requires the solution of a stochastic differential equation with boundary conditions, which, often, is not Markovian. We propose a wavelet-collocation algorithm for solving a Milstein approximation to the stochastic boundary problem. Its convergence properties are studied. Furthermore, we value boundary-linked derivatives using Malliavin calculus and Monte Carlo methods. We apply these ideas to value European call options of boundary-linked asset

Worst-case estimation and asymptotic theory for models with unobservables

This paper proposes a worst-case approach for estimating econometric models containing unobservable variables. Worst-case estimators are robust against the adverse effects of unobservables. In contrast to the classical literature, there are no assumptions about the statistical nature of the unobservables in a worst-case estimation. This method is robust with respect to the unknown probability distribution of the unobservables and should be seen as a complement to standard methods, as cautious modelers should compare different estimations to determine robust models. The limit theory is obtained. A Monte Carlo study of finite sample properties has been conducted. An economic application is included

Computing continuous-time growth models with boundary conditions via wavelets.

This paper presents an algorithm for solving boundary value differential equations, which often arise in economics from the application of Pontryagin’s maximum principle. We propose a wavelet-collocation algorithm, study its convergence properties and illustrate how this approach can be applied to different economic problemsWavelets; Continuous-time growth models; Boundary value problems;

VALUATION OF BOUNDARY-LINKED ASSETS

This article studies the valuation of boundary-linked assets and their derivatives in continuous-time markets. Valuing boundary-linked assets requires the solution of a stochastic differential equation with boundary conditions, which, often, is not Markovian. We propose a wavelet-collocation algorithm for solving a Milstein approximation to the stochastic boundary problem. Its convergence properties are studied. Furthermore, we value boundary-linked derivatives using Malliavin calculus and Monte Carlo methods. We apply these ideas to value European call options of boundary-linked assets.

COMPUTING CONTINUOUS-TIME GROWTH MODELS WITH BOUNDARY CONDITIONS VIA WAVELETS

This paper presents an algorithm for approximating the solution of deterministic/stochastic continuous-time growth models based on the Euler's equation and the transversality conditions. The main issue for computing these models is to deal efficiently with the boundary conditions associated. This approach is a wavelets-collocation method derived from the finite-iterative trapezoidal approach. Illustrative examples are given.

Do business density and variety determine retail performance?

Outlet location plays a crucial role in retail strategy. In this paper we study the relationship between spatial density (concentration) of retailers in the trade area and their economic performance. This analysis will help managers figure out the economic potential of starting a retail business in a given area, reducing business start-up risks. We find that retail businesses located in high and low retail density zones enjoy higher performance levels, consistent with competitive advantage arising from agglomeration economies and local market power respectively. We also find that retail businesses located in intermediate density areas use a differentiation strategy based on business variety (diversification across stores). Outlets located in areas with the highest variety enjoy performance levels similar to those achieved in the agglomeration and low density areas. The results suggest that retail companies should jointly consider variety and density to determine location

Worst-case estimation for econometric models with unobservable components.

A worst-case estimator for econometric models containing unobservable components, based on minimax principles for optimal selection of parameters, is proposed. Worst-case estimators are robust against the averse effects of unobservables. Computing worstcase estimators involves solving a minimax continuous problem, which is quite a challenging task. Large sample theory is considered, and a Monte Carlo study of finite-sample properties is conducted. A financial application is consideredWorst-case decision; Robust modelling; Minimax optimization;

WORST-CASE ESTIMATION AND ASYMPTOTIC THEORY FOR MODELS WITH UNOBSERVABLES

This paper proposes a worst-case approach for estimating econometric models containing unobservable variables. Worst-case estimators are robust against the adverse effects of unobservables. In contrast to the classical literature, there are no assumptions about the statistical nature of the unobservables in a worst-case estimation. This method is robust with respect to the unknown probability distribution of the unobservables and should be seen as a complement to standard methods, as cautious modelers should compare different estimations to determine robust models. The limit theory is obtained. A Monte Carlo study of finite sample properties has been conducted. An economic application is included.

The long memory of newspapers' subscriptions: between the short-run and persistence response

The mainstream of marketing time series analysis has shifted from classical short-range dependence (ARMA, transfer functions and VAR models). However, in cases where purchase decisions entail some commitment (e.g., a subscription selling periodic use of a product or service), sales response entails a long-term effect is not permanent. Long-memory assumes that shocks to a time series have neither a persistent nor a short-run transitory effect, but that they last for a long time and decay slowly with time. Many marketing policies face a short-memory response at the individual customer level but display a considerable degree of persistence at the aggregate level. The aggregation of short-run individual decisions made by heterogeneous customers can show a long-memory pattern. In today's highly competitive newspaper industry, loyal, ongoing customers are a key to obtain stable and long-term profits. Often newspapers obtain a loyal customer base through subscriptions. This paper proposes a long-memory model to study the long-term sales response dynamics in subscription markets. The model accounts for the heterogeneity of the individual responses and distinguishes between both trend and long-memory components pattern of subscriptions. This model permits more accurate predictions of subscription sales than those obtained using persistence models.